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Density of the lexicographically ordered space $ \{0,1\}\sp \alpha$


Author: W. W. Comfort
Journal: Proc. Amer. Math. Soc. 109 (1990), 523-525
MSC: Primary 54A25; Secondary 54F05
DOI: https://doi.org/10.1090/S0002-9939-1990-1000150-9
MathSciNet review: 1000150
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Abstract: For an infinite cardinal $ \alpha $, the lexicographically ordered space $ {\left\{ {0,1} \right\}^\alpha }$ is denoted $ \Lambda (\alpha )$; its density is denoted $ d\Lambda (\alpha )$. Completing a computation left unfinished elsewhere, we prove $ d\Lambda (\alpha ) = {2^{_\smile ^\alpha }}$.


References [Enhancements On Off] (What's this?)

  • [1] W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 211. MR 0396267
  • [2] W. W. Comfort and D. Remus, Long chains of Hausdorff topological group topologies,(submitted for publication).
  • [3] M. A. Maurice, Compact ordered spaces, Mathematical Centre Tracts, no. 6, Mathematisch Centrum, Amsterdam, 1964.
  • [4] Wacław Sierpiński, Sur une propriété des ensembles ordonnés, Fund. Math. 36 (1949), 56–67 (French). MR 0031528

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1000150-9
Keywords: Density, lexicographic order
Article copyright: © Copyright 1990 American Mathematical Society